General decay and blowup of solutions for coupled viscoelastic equation of Kirchhoff type with degenerate damping terms
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DOI: 10.1002/mma.5429
Abstract: In this work, we consider a nonlinear system of viscoelastic equations of Kirchhoff type with degenerate damping and source terms in a bounded domain. Under suitable assumptions on the initial data, the relaxation functions gi(i … read more here.
Keywords: damping terms; degenerate damping; type degenerate; kirchhoff type ... See more keywords
Nonconforming quadrilateral finite element method for nonlinear Kirchhoff‐type equation with damping
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DOI: 10.1002/mma.6065
Abstract: Nonconforming quadrilateral EQ1rot finite element method (FEM) of nonlinear Kirchhoff‐type equation with damping is studied on anisotropic meshes. Based on the property of the nonlocal term of this equation, unconditional optimal error estimates of O(h)… read more here.
Keywords: kirchhoff type; equation; nonconforming quadrilateral; type equation ... See more keywords
Ground State Solutions for Asymptotically Periodic Kirchhoff-Type Equations with Asymptotically Cubic or Super-cubic Nonlinearities
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DOI: 10.1007/s00009-017-1010-y
Abstract: This paper is concerned with the following Kirchhoff-type equation $$\begin{aligned} -\left( a+b\int _{\mathbb {R}^3}|\nabla {u}|^2\mathrm {d}x\right) \triangle u+V(x)u=f(x, u), \quad x\in \mathbb {R}^{3}, \end{aligned}$$-a+b∫R3|∇u|2dx▵u+V(x)u=f(x,u),x∈R3,where $$V\in \mathcal {C}(\mathbb {R}^{3}, (0,\infty ))$$V∈C(R3,(0,∞)), $$f\in \mathcal {C}({\mathbb {R}}^{3}\times \mathbb… read more here.
Keywords: tau; asymptotically periodic; frac; mathbb ... See more keywords
Existence of Multiple Solutions of a Kirchhoff Type $p$-Laplacian Equation on the Sierpiński Gasket
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DOI: 10.1007/s10440-019-00283-z
Abstract: In this paper, we study the following boundary value problem involving the weak $p$-Laplacian. $$ -M\bigl(\|u\|_{\mathcal{E}_{p}}^{p}\bigr)\Delta _{p} u = h(x,u) \quad \text{in}\ \mathcal{S}\setminus \mathcal{S}_{0}; \quad u = 0 \ \text{on}\ \mathcal{S}_{0}, $$ where $\mathcal{S}$ is… read more here.
Keywords: multiple solutions; kirchhoff type; existence multiple; solutions kirchhoff ... See more keywords
Infinitely many sign-changing solutions to Kirchhoff-type equations
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DOI: 10.1007/s13324-018-0218-8
Abstract: In this paper we study the existence of multiple sign-changing solutions for the following nonlocal Kirchhoff-type boundary value problem: $$\begin{aligned} \left\{ \begin{array}{ll} -\left( a+b\int _{\Omega }|\nabla u|^2{ dx}\right) \triangle {u}=\lambda |u|^{p-1}u,&{}\quad \text{ in }\quad \Omega… read more here.
Keywords: kirchhoff type; infinitely many; sign changing; changing solutions ... See more keywords
Nontrivial Weak Solution for a Schrödinger–Kirchhoff-Type System Driven by a $$(p_1,p_2)$$(p1,p2)-Laplacian Operator
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DOI: 10.1007/s41980-018-0017-x
Abstract: In this paper, we investigate the existence of nontrivial weak solution for a Schrödinger–Kirchhoff-type system driven by a $$(p_1,p_2)$$(p1,p2)-Laplacian operator under appropriate hypotheses. The proofs are based on the variational methods. read more here.
Keywords: dinger kirchhoff; kirchhoff type; weak solution; nontrivial weak ... See more keywords
On a Class of Critical p-Biharmonic Kirchhoff Type Problems with Indefinite Weights
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DOI: 10.1007/s41980-020-00436-z
Abstract: Using the genus theory introduced by Krasnoselskii and a variant of the mountain pass theorem due to Rabinowitz [24], we study the existence of solutions for the following Kirchhoff type problem: $$\begin{aligned} {\left\{ \begin{array}{ll} M\left(… read more here.
Keywords: class critical; kirchhoff; delta; partial partial ... See more keywords
On Kirchhoff type equations with critical Sobolev exponent
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DOI: 10.1016/j.jmaa.2018.02.023
Abstract: We study the following Brezis-Nirenberg problem of Kirchhoff type $$ \left\{\aligned &-(a+b\int_{\Omega}|\nabla u|^2dx)\Delta u = \lambda|u|^{q-2}u + \delta |u|^{2}u, &\quad \text{in}\ \Omega, \\ &u=0,& \text{on}\ \partial\Omega, \endaligned \right. $$ where $\Omega\subset \bbr^4$ is a bounded… read more here.
Keywords: critical sobolev; equations critical; type equations; sobolev exponent ... See more keywords
Bounded state solution of degenerate Kirchhoff type problem with a critical exponent
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DOI: 10.1016/j.jmaa.2019.06.013
Abstract: Abstract In the present paper, we investigate the following degenerate Kirchhoff type problem { − ( b ∫ R N | ∇ u | 2 d x ) Δ u + V ( x )… read more here.
Keywords: kirchhoff type; problem; type problem; critical exponent ... See more keywords
Sign-changing and nontrivial solutions for a class of Kirchhoff-type problems
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DOI: 10.1016/j.jmaa.2019.123476
Abstract: Abstract In this paper, we study the existence of sign-changing (nodal) and nontrivial solutions for the nonlinear Kirchhoff-type equation { − ( a + b ∫ Ω | ∇ u | 2 d x )… read more here.
Keywords: nontrivial solutions; solutions class; sign changing; changing nontrivial ... See more keywords
Ground-state solutions to Kirchhoff-type transmission problems with critical perturbation
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DOI: 10.1016/j.jmaa.2019.123568
Abstract: Abstract A class of Kirchhoff-type transmission problems with critical perturbation is studied. Unlike other studies on elliptical equations with critical growth, a ground-state solution is obtained using a perturbation method instead of verifying that the… read more here.
Keywords: perturbation; transmission problems; critical perturbation; problems critical ... See more keywords